Real and Functional Analysis by Serge Lang
This book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its understanding, for instance, my Undergraduate Anal- ysis. I assume that the reader is acquainted with notions of uniform con- vergence and the like. In this third edition, I have reorganized the book by covering inte- gration before functional analysis. Such a rearrangement fits the way courses are taught in all the places I know of. I have added a number of examples and exercises, as well as some material about integration on the real line (e.g. on Dirac sequence approximation and on Fourier analysis), and some material on functional analysis (e.g. the theory of the Gelfand transform in Chapter XVI). These upgrade previous exercises to sections in the text. In a sense, the subject matter covers the same topics as elementary calculus, viz. linear algebra, differentiation and integration. This time, however, these subjects are treated in a manner suitable for the training of professionals, i.e. people who will use the tools in further investiga- tions, be it in mathematics, or physics, or what have you. In the first part, we begin with point set topology, essential for all analysis, and we cover the most important results.-
Algebraic Geometry
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Introduction to Riemannian Manifolds
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Algebra
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Brownian Motion and Stochastic Calculus
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Applications of Lie Groups to Differential Equations
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The Arithmetic of Elliptic Curves
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Advanced Linear Algebra
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Groups and Representations
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Modular Functions and Dirichlet Series in Number Theory
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Categories for the Working Mathematician
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Quaternion Algebras
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Measure, Integration & Real Analysis
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Differential Forms in Algebraic Topology
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Complex Analysis
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Modern Graph Theory
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Problems in Analytic Number Theory
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Representation Theory
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Fermat's Last Theorem
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Holomorphic Functions and Integral Representations in Several Complex Variables
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Elements of Homotopy Theory
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Graph Theory
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Probability Theory I
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Algebraic Number Theory
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Topology and Geometry
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Foundations of Differentiable Manifolds and Lie Groups
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Abstract Algebra
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Introduction to Topological Manifolds
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Linear Representations of Finite Groups
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A Classical Introduction to Modern Number Theory
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Introduction to Smooth Manifolds
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Brownian Motion, Martingales, and Stochastic Calculus
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Lie Groups, Lie Algebras, and Representations
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Functions of One Complex Variable I
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A First Course in Modular Forms
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Commutative Algebra
| SKU | Unavailable |
| ISBN 13 | 9781461269380 |
| ISBN 10 | 1461269385 |
| Title | Real and Functional Analysis |
| Author | Serge Lang |
| Series | Graduate Texts In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer-Verlag New York Inc. |
| Year published | 2012-10-23 |
| Number of pages | 580 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |